Savage 110/Steven's 200 Yes.
But start with a .22Lr and get the mechanics of aiming down using cheap ammo.
Start with a bolt action; those are cheaper. Also (and this is personal opinion)--semi-autos can make you lazy. And bad habits set in fast if you are first learning and practicing bad form. If you have to hand cycle a bolt to take a second shot, you tend to pay more attention the second time around.
If your hunting will include animals something larger than a bread box, you can choose a larger caliber later.